Research in Photonics - Applied Mathematics Laboratory at the … · Members - Applied Mathematics Laboratory A.D Bandrauk. Canada Research Chair in Computational Photonics, Fellow

Research Photonics

Research in Photonics - Applied Mathematics

Laboratory at the CRM

Emmanuel Lorin

Carleton University/ Centre de Recherches Mathématiques

Atelier Maillage Industriel du CRM, Septembre 2015

Lorin et al. Research Photonics

Research Photonics

Members - Applied Mathematics Laboratory

A.D Bandrauk. Canada Research Chair in ComputationalPhotonics, Fellow SIAM. Professor in Theoretical Chemistry atUniversité de Sherbrooke. Laser physics, photonics, quantumchemistry, high performance computing.

E. Lorin. Professor in Applied Mathematics, CarletonUniversity, Ottawa. Numerical analysis, PDE, mathematicalphysics, modeling in nonlinear optics, photonics, highperformance computing.

+ students MSc+PhD, post-docs, research associates.

Organization of workshops, international collaborations in appliedmathematics, physics, industry,...

Lorin et al. Research Photonics

Research Photonics

Research Topics - Physics

Attosecond Science

Laser-atom/molecule interaction: intense (I > 1013W·cm−2)and short (femtosecond) laser pulsesAttosecond pulse generation: 3-step model. [Corkum, P. & Krausz, F.

Nature Phys. 3, 381â387 (2007)].

Figure : High Harmonics Generation

Cut-o frequency for hydrogen: 3.17Up + IpLorin et al. Research Photonics

Research Photonics

Attosecond Science

Generation of attosecond pulse train: [Nisoli, M., Nature Photonics 5, '11].

Figure : Attosecond pulse train

Lorin et al. Research Photonics

Research Photonics

Attosecond Science

Electron control using short & intense laser pulses: AttosecondScience.

Short laser pulses with intensity > internal electric eld ofatoms and molecules, E = 5× 109V·cm−1, equivalentI = 3.5× 1016W·cm−2.Timescale Orbital period of electron in H: ∼ 100 attoseconds> shortest experimental attosecond pulse ever generated ∼ 50attoseconds.

Modeling & Simulation: Schrödinger, Maxwell-Schrödinger,...,circularly polarized pulses, etc.

Lorin et al. Research Photonics

Research Photonics

Nonperturbative nonlinear optics

Nonperturbative nonlinear optics (lamentation)

Propagation (macro/multiscale) short/intenses pulse in gas.

Nonperturbative regime, where usual NLO models (NLSE) fail.

Filamentation-laser.

Denition (Couairon, Mysyrovicz, Phys. Report 441, 2007)

Filament or lamentation denotes electromagnetic structure with

intense core, able to propagate over extended distances much

larger than typical diraction length while keeping a narrow beam

size without the help of any external mechanism.

Lorin et al. Research Photonics

Research Photonics

Applications: Filamentation

Equilibrium between following ingredients (?):

(cubic)Kerr [self-focus.] - plasma [defocus.]

FILAMENT

INTENSITY

ULTRASHORTAND INTENSELASER

INCREASING

PLASMA(IONIZATION)

(DUE TO PLASMA)DEFOCUSING

Z

FOCUSING+ SELF−FOC. (REFRACTION−KERR EFFECT)

SELF−FOCUS. (KERR EFFECT)

Figure : Evolution of single lament envelope

Propagation in a gas: lamentation L. Bergé, et al., Rep. on Prog. in Phys.

70 ('07), A. Couairon, A. Mysyrovicz, Phys. Report 441 ('07)

Applications: communication, spectroscopy, military applications,atmospheric science (lightning control)

Lorin et al. Research Photonics

Research Photonics

Filamentation

Nonperturbative models: high order nonlinearities + ionization

Figure : Workshop CRM-Filamentation 2014

Lorin et al. Research Photonics

Research Photonics

Pair Production

Production of pairs of particle/antiparticle

Dirac equation (relativistic version of Schrödinger), Dirac-Maxwell.Schwinger's eect. Experiments at ALLS - INRS-Varennes.

Lorin et al. Research Photonics

Research Photonics

Research Topics - Applied Mathematics

Mathematical and numerical methods

Analysis and modeling, Partial Dierential Equations (PDE):Schrödinger, Dirac, Maxwell.

Numerical simulations Simulations: nite element, nitevolume, spectral methods.

Domain decomposition methods (Schwarz WaveformRelaxation) for quantum/classical wave problems.

Absorbing boundary conditions for wave equations in truncateddomains.

Adaptive mesh renement (multiresolution analysis).

High order splitting methods.

Continuous (stochastic) optimization.

Lorin et al. Research Photonics

Research Photonics

Research Topics - Applied Mathematics

High Performance Computing. Mammouth (Compute Canada,RQCHP)

39 168 CPU cores de calcul with three dierent congurations

1588 SGI C2112-4G3 compute nodes: two AMD 12 core

processors AMD at 2.1 GHz Memory: 32 GB

20 SGI H2106-G7 compute nodes: four AMD 12 core

processors at 2.2 GHz Memory: 256 GB

2 SGI H2106-G7 compute nodes: four AMD 12 core processors

at 2.2 GHz Memory: 512 GB

Inniband QDR network that is non-blocking among 216 nodes

and 3.5:1 oversubscribed for the rest of the cluster Operating

System : CentOS 6.4

The theoretical peak performance of the system is 240.3TFLOP/s. The total memory of the system is 57.6 TB.

Lorin et al. Research Photonics

Research Photonics

Micro-Macro Model

Example 1 - Maxwell-Schrödinger model; coupling 3-D Maxwell eq.with > 100, 000 Schrödinger eq. [Lorin, et al., Comput. Phys. Comm. vol. 177 ('07)]

∂tB(r, t) = −c∇× E(r, t)∂tE(r, t) = c∇× B(r, t)− ∂tP(r, t)− J(r, t)∇ · B(r, t) = 0∇ ·(E(r, t) + P(r, t)

)= 0

P(r, t) = N (r)∑m

i=1pi (r, t) = N (r)

∑mi=1

χΩi(r)∫R3 ψi r

′ψ∗ii∂tψi (r

′, t) = −4r′ψi + r′ · Eri

ψi + Vcψi

Lorin et al. Research Photonics

Research Photonics

Geometrical conguration

z

x

y

Gas divided in small volumes

x

y

z

H2+

ZOOM

Incoming laser pulse

|ψ| 2

ndv molecules

Figure : Model geometry - P.-I.-C. approach

In each cell: Polarization deduced from dipole moment: P = Np.

Lorin et al. Research Photonics

Research Photonics

Attosecond Science: circularly polarized pulse

Example 2 - circularly polarized pulse - Molecule H2, HHe+

Lorin et al. Research Photonics